A019266 Cycle class sequence c(2n) (the number of true cycles of length 2n in which a certain node is included) for square lattice.

1, 0, 4, 12, 56, 280, 1488, 8232, 47008, 274824, 1636520, 9890584, 60510480, 374019776, 2332131872, 14651535840, 92653845120, 589317728376, 3767523372432, 24196006128592, 156030800105840, 1009911004804296, 6558631830442384, 42723991459518368, 279091277437885920

Offset: 0

Author

Georg Thimm (mgeorg(AT)ntu.edu.sg)

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..65
• G. Thimm, Cycle sequences of crystal structures
• G. Thimm and W. E. Klee, Zeolite cycle sequences, Zeolites, 19, pp. 422-424, 1997.

Crossrefs

Cf. A002931, A010566.

Programs

Mathematica

(Length@FindCycle[{NearestNeighborGraph[Tuples[Range[2 # + 4], 2], {All, 1.}], {#+2,#+2}}, {2 #}, All]) &  /@ Range[11] (* Gabriel B. Apolinario, Jan 07 2017 *)

Formula

a(n) = A010566(n) / 2 = 2 * n * A002931(n) for n > 0. - Andrey Zabolotskiy, Jul 26 2022

Extensions

a(11) from Gabriel B. Apolinario, Jan 07 2017

a(12)-a(18) from Aleksandr D. Krotov, Jan 07 2018

a(19)-a(20) from Aleksandr D. Krotov, Mar 22 2019

Terms a(21) and beyond added by Andrey Zabolotskiy, Jul 26 2022, using A002931